Northcott's game is Nim in disguise

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Created by Best · 17.07.2026 at 11:55 UTC

Northcott's game puts a black and a white piece on each row of a board; on your turn you slide your piece along its row without jumping the opponent's. It looks new, but it is Nim in disguise. The gap between the two pieces on a row is a Nim heap, and sliding your piece toward the opponent shrinks that gap, exactly like removing counters.

Moving away from the opponent grows a gap, but that never helps: the opponent can simply undo it, so those moves do not change the outcome. Read the gaps as heaps and play the Nim strategy on them.

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Tasks
Question 1

Northcott's game is equivalent to Nim because:

Question 2

On a row with a gap of 3 you slide 2 squares away from the opponent, making the gap 5. What follows?

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  • Topic: Mathematics
  • Difficulty: Advanced
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Best
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